Casimir and short range gravity tests Astrid Lambrecht and Serge Reynaud with A. Canaguier-Durand, R. Guérout, J. Lussange, A. Gérardin collaborations M.-T. Jaekel (ENS Paris), J. Chevrier (I. Néel Grenoble), V.V. Nesvizhevsky (ILL Grenoble), C. Genet, T. Ebbesen (Strasbourg), P.A. Maia Neto (Rio de Janeiro), G.-L. Ingold (Augsburg), D. Dalvit (Los Alamos), H.B. Chan (Hong-Kong) … ESF network “CASIMIR” http://www.casimir-network.com

Moriond / GPhyS March 2011

http://www.lkb.ens.fr

CNRS, ENS, UPMC

Search for scale dependent modifications of the gravity force law Excluded domain in the plane (λ,α)

The exclusion plot for deviations with a Yukawa form Geophysical

Windows remain open for deviations at short ranges or long ranges

log10

Laboratory Satellites

log10 (m)

LLR

Planetary

Courtesy : J. Coy, E. Fischbach, R. Hellings, C. Talmadge & E. M. Standish (2003) ; see M.T. Jaekel & S. Reynaud IJMP A20 (2005) Talk E. Fischbach, common session with QCD conf

Constraints at sub-mm scales 

10µm <  : Short range gravity measurements Talk E. Adelberger



0.1µm <  < 10µm : Casimir experiments the present talk



 < 0.1µm : Neutron physics Talk V. Nesvizhevsky



See also the projects with cold atoms Talk B. Pelle

Exclusion plot for spin-independent interactions

Overview I. Antoniadis, S. Baessler, .. V. Nesvizhevsky et al, to appear (2011)

The challenge of Casimir tests For two Cu plates 1mm thick, Casimir dominates Newton when L < 10µm The hypothetical new force would be seen as a difference between experiment and theory

Casimir

Newton Yukawa m

F new  F exp  F th L The accuracy of theory and experiment have to be assessed independently A. Lambrecht et al, in “Casimir physics” (2011) [arXiv:1006.2959]

m

The “vacuum energy catastrophe” 

1900 : Planck solves the puzzle of blackbody radiation



1912 : Planck introduces vacuum fluctuations (zero-point fluctuations)



1925-… : Quantum Mechanics and Quantum Field Theory confirm the existence and effects of vacuum fluctuations

A major problem for fundamental physics identified by Nernst in 1916, still unsolved today : The mean energy density per unit volume of “empty space” is much too large to be compatible with gravity observations for any reasonable cutoff frequency R.J. Adler, B. Casey and O.C. Jacob, Am. J. Phys. 63 (1995) 620

A common “solution” : the denial of vacuum energy Quoting Pauli « For fields [in contrast to the material oscillator], it is more consistent not to introduce the zero-point energy … For, on the one hand, the latter would give rise to an infinitely large energy per unit volume due to the infinite number of degrees of freedom ... and, as is evident from experience, it does not produce any gravitational field ... And, on the other hand, it would be unobservable since it cannot be emitted, absorbed or scattered, and hence, cannot be contained within walls. » W. Pauli, Die Allgemeinen Prinzipien der Wellenmechanik (Springer, 1933)

The Casimir force (ideal case) A universal effect from confinement of vacuum fluctuations : it depends only on ћ, c, and geometry



Here written for   



Parallel plane mirrors Perfect reflection Null temperature

Attractive force (negative pressure)

H.B.G. Casimir, Proc. K. Ned. Akad. Wet. (Phys.) 51 (1948) 79

The Casimir force between “real mirrors” 

Real mirrors not perfectly reflecting 



Experiments performed at room temperature 



Casimir force depends on non universal properties of the material plates used in the experiments

Effect of thermal field fluctuations to be added to that of vacuum fluctuations

Experiments not done in the ideal Casimir geometry 



Plane-sphere geometry used for all recent precise experiments Surface state not perfect : patches, contamination, roughness … A. Lambrecht et al, in “Casimir physics” (2011) [arXiv:1006.2959]

Calculation of the Casimir force .. 

Casimir physics : mechanical effects of the coupling of mirrors to vacuum (and thermal) fluctuations  



Mirrors described by their EM scattering properties Confinement of vacuum fluctuations in the cavity affects the radiation pressure and produces the Casimir effect

The “scattering approach” 



Used for years for evaluating the Casimir force between non perfectly reflecting mirrors Today the best solution for calculating the Casimir force in arbitrary geometries

M. Jaekel, S. Reynaud, J. Physique I-1 (1991) 1395 quant-ph/0101067 A. Lambrecht, S. Reynaud EPJD 8 (2000) 309 quant-ph/9907105 A. Lambrecht, P. Maia Neto & S. Reynaud, New J. Physics 8 (2006) 243

.. Calculation of the Casimir force 

Electromagnetic fields in 3d space





Plane parallel but not perfectly reflecting mirrors : specular reflection amplitudes depending on frequency , polarization p, incidence angle  Lateral components of the wavevector preserved Wick rotation from real to imaginary frequencies



Some “details” to be treated with great care





Evanescent modes contribute



Dissipation has to be accounted for

General expression for the free energy

Models for reflection amplitudes 





Lifshitz formula reproduced for  bulk mirror described by a local dielectric response function  reflection given by Fresnel laws Dielectric function Ideal Casimir formula recovered for  r → 1 and T → 0 The scattering formula accommodates more general expressions for the reflection amplitudes  finite thickness  multilayer structure  non local dielectric response  non isotropic response  chiral materials …

Plasma model

Drude model

A. Lambrecht, P. Maia Neto & S. Reynaud, New J. Physics 8 (2006) 243

Material dependence 

The plasma model is the simplest model for metals 





No dissipation for conduction electrons 1 10

Only one length scale, the plasma wavelength

ηF 

perfect mirrors limit

0

Interband transitions neglected

T  0K

-1 0.1 10

Force reduced wrt Casimir formula

plasma model plasma Lplasmon 2µm



Only a small correlation between plasma and thermal effects

1.0 0.9 0.8 0.7 0.6 0.5 0.1

plasma model, T  0 K 1.0

C. Genet, A. Lambrecht & S. Reynaud, Phys. Rev. A 62, 012110 (2000)

10.0

Finite temperature and dissipation 

Strong correlation between thermal and dissipation effects M. Boström and B.E. Sernelius, Phys. Rev. Lett. 84 (2000) 4757 20

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Large difference (by a factor 2) at large distances F between =0 and ≠0 FCas

10 5 2 1 0.5



Thermal contribution negative at some distances for ≠0

0.2 0.1 0.01 0.02

0.05 0.1 0.2

0.5

1 2 LL[µm] [ m]

5

10

20

G. Ingold, A. Lambrecht, S. Reynaud, Phys. Rev. E80 (2009) 041113

50 100

The plane-sphere geometry beyond PFA 

General scattering formula

reflection matrix on the plane mirror reflection matrix on the sphere (Mie scattering of vacuum and thermal fluctuations)







transformation from plane to spherical waves

This is an “exact” multipolar series of the free energy o o

Sums are truncated at some

for the numerics

The numerical results are accurate for not too large spheres

P.A. Maia Neto, A. Lambrecht, S. Reynaud, Phys. Rev. A 78 (2008) 012115

Correlation geometry - temperature dissipation Force between metallic plane and sphere at room temperature 2 Drawn as the ratio of force for plasma model to force for Drude model



Ratio at large L never approaches the factor 2 given by PFA

plasma

The two results are always closer than expected from PFA

1.6 1.4

F



/F

Drude

1.8

R = 0.1 μm R = 0.2 μm R = 0.5 μm R = 1 μm R = 2 μm R = 5 μm R = 10 μm PFA

1.2 1 0.5

1

2 L [μm]

5

A. Canaguier-Durand, P.A. Maia Neto, A. Lambrecht, S. Reynaud PRL 104 (2010) 040403

10

Casimir experiments 

Recent precise experiments : dynamic measurements of the resonance frequency of a microresonator



Shift of the resonance gives the gradient of Casimir force Courtesy R.S. Decca et al (Indiana U – Purdue U Indianapolis)

After years of improvement in experiments and theory, an unexpected problem in their comparison !

R.S. Decca, D. Lopez, E. Fischbach et al, Phys. Rev. D75 (2007) 077101

Comparison with theory Results fit predictions of the plasma model (not the Drude model !)

Courtesy R.S. Decca et al

But Gold has a finite conductivity so that ≠0 R.S. Decca, D. Lopez, E. Fischbach et al, Phys. Rev. D75 (2007) 077101

Another recent experiment at Yale 





Purdue experiments favor the plasma model at distances 0.16-0.75µm where the thermal effect is small

A new experiment at Yale at larger distances 0.7-7µm where the thermal F effect is larger FCas Results favor the Drude model after subtraction of a large contribution of the patch effect

20 10 5 2 1 0.5 0.2 0.1 0.01 0.02

0.05 0.1 0.2

0.5

1 2 LL[µm] [ m]

5

10

20

50 100

A.O. Sushkov, W.J. Kim, D.A.R. Dalvit, S.K. Lamoreaux, Nature Phys. 6 Feb 2011

Some conclusions 

The new results of the Yale experiment 

see the thermal contribution



fit the expected Drude model



need to be confirmed K. Milton, News & Views Nature Phys. 6 Feb 2011



Electrostatic patch effect is a source of concern in a number of measurements C.C. Speake and C. Trenkel, PRL 90 (2003) 160403 

solution : measure (or at least estimate) the patch distribution

Casimir effect verified, but not with an accuracy at the % level Casimir tests of short range gravity have still to be improved …

Thanks for your attention